In 1897, 13-year-old Curtis qualified fourth in her first appearance at the U.S. Women's Amateur. In 1906 her sister Harriot won the Championship. Although health problems had prevented Margaret from competing for several years, she captured her first of three U.S. championships in 1907 by beating her sister in the finals. That year she played in England and in a stroke-play tournament at Walton Heath, near London, she was leading playing partner May Hezlet by five stokes going into the final hole. Curtis hit her drive into gorse bush, a very spiny and dense evergreen shrub common throughout western Europe but unfamiliar to an American. Curtis ended up taking a disastrous 13 on the hole to lose the tournament.

Besides her skill at golf, Curtis was an excellent tennis player. In 1908 she won the U.S. Open doubles tennis championship with Evelyn Sears, becoming the only woman to simultaneously hold the U.S. golf and tennis titles.

In 1904, Curtis was a student at Simmons College School of Social Work in Boston, training that would lead to her being a Board member of the Family Service Society for 51 years. With her career over in competitive golf, during World War I, she went to Paris, France where she joined the Red Cross, serving as the head of its Bureau for Refugees for three years. Her time in Paris marked the beginning of several more years spent in various places across Europe with the Red Cross.

In 1932, Curtis and her sister donated the Curtis Cup for a biennial golf competition between amateur teams representing the United States and Great Britain. She remained active in golf matters for most of her life. In December 1955, the Women's Golf Association of Massachusetts established a tournament in her and her sister's honor. The trophy, known as "The Curtis Bowl," is a replica of the Curtis Cup.